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In this work, governing equations of the feed line, cut-off valve, and the starter system are analyzed mathematically and numerically. In the mathematical solution, the stability of the valve system is considered using the Laplace transform along with the linearization of the equations of the system. According to parameter design of the feed pipe–valve system, the system demonstrates the stable behavior in the effective parameter of the valve system on the basis of the Nyquist and Bode stability criterion. In the numerical solution, the steady state behavior of the cut-off valve is simulated during the cut-command. Then the rate of the pressure variation, mass flow rate through of the valve, gas pressure of the starter system, and the upstream pressure of the valve (water hammer) are considered based on the valve's poppet motion. The comparison of the simulation results with the experimental data depicts only 13 percent error in the mass flow rate through of the valve. In the last time of the closing valve, there is no variation in the mass flow rate in the valve due to the excessive loss factor of the valve when the valve approximately is closed. The results show that the closure of the cutoff valve shall be provided in accordance with allowable maximum pressure of the hydraulic shock on the established

Keywords: Cut-off Valve, Mathematical modeling, Liquid Propellant Rocket Engine, Stability analysis

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